you want to give read and write access permission for a folder to a particular system in the LAN. (you did not mention the type of network, work group or domain)
*use share permissions to provide read and write access permission to the folder while adding the entity select the object type as "computers"
search and include the computer which you want to provide the access
*use the security tab and include the same computer which you want to provide the access.set the administration permissions accordingly. 8)
sorry i was providing the basic sharing steps
If it is a domain network you need to specify one thing - login credentials used by the user of that pc is it a local login on that system or an AD login?